7) The Week Problem
Continuous Weeks or Recurring Dates?

The month problem asks which scale Mars should preserve. The week problem is less forgiving: it asks what happens when two forms of regularity cannot both survive.

On Earth, the seven-day week simply continues. Sunday is followed by Monday whether a month ends, a year ends or February acquires an extra day. Calendar dates move underneath that uninterrupted sequence, which is why 1 January can fall on different weekdays in different years.

A Martian calendar could work exactly the same way. But it does not have to.

If months are designed carefully, every month can instead begin on the same weekday and every valid numerical date can always occupy the same weekday position. The price is that, at certain boundaries, the civil weekday naming sequence cannot continue through all seven positions.

Both arrangements are regular. They are simply regular in different ways.

That is the week problem.

Two kinds of regularity

The first property is continuous weekly succession. The seven weekday positions repeat indefinitely: Day 7 is always followed by Day 1, regardless of where months and years begin. The calendar never interferes with the sequence. This is the Gregorian arrangement.

The second property is recurring date–weekday alignment. Under this arrangement, if Day 8 of Month 4 is the second weekday this year, it remains the second weekday next year. If every month begins on the first weekday, the internal calendar pattern can repeat indefinitely.

Earth gives us the first property but not the second. Gregorian months contain 28, 29, 30 or 31 days. Only 28 divides exactly by seven, so most month boundaries move the weekday on which the next month begins. A common year is 52 weeks plus one day, and leap years shift it further.

We are so used to this that it barely registers. A meeting on 15 September requires us to know which weekday 15 September happens to occupy this year. A weekday-based monthly rota cannot simply be reused forever. Every new year needs a new calendar layout.

Modern software makes the inconvenience trivial. That does not make the underlying trade-off disappear.

If we were designing a civil calendar from scratch, we could instead decide that recurring dates should retain fixed weekday positions. Monthly layouts would repeat, annual templates would be more reusable and the date itself would carry more information.

The cost is equally clear. If a month does not contain a whole number of seven-sol weeks, preserving the next month start requires doing something to the weekday sequence.

The choice is therefore not between order and disorder. It is between two kinds of order.

Levitt and Darian choose the date

Levitt encountered the problem directly. His 56-sol months are easy:

56 = 8 × 7

Eight complete seven-sol weeks fit exactly.

The difficulty lies in the 55-sol months. If the seven-position weekday sequence simply continued, the next month would begin one weekday earlier than the month before it and the repeating month structure would immediately start to drift.

Levitt chose recurrence. The final civil week of a 55-sol month contains six weekday positions rather than seven. The following physical sol begins the next month and receives the first weekday label.

That wording matters. No physical Martian sol disappears. Mars does not rotate six times one week and then wait politely while the calendar catches up. Elapsed time proceeds normally; sunrise, sunset and human biological rhythms proceed normally.

Only the civil weekday naming sequence is interrupted.

Under a continuously repeating seven-position sequence, the next physical sol would have occupied Day 7. Levitt instead gives it the Day 1 label because the new month has begun. The result is a perpetual civil structure in which every month starts in the same place and every valid numerical date retains the same weekday relationship.

Darian makes essentially the same choice at a different scale. Its ordinary 28-sol months contain four complete seven-sol weeks. Shortened 27-sol months contain three complete weeks followed by a six-position terminal week, after which the following month begins again on the first weekday.

Levitt and Darian therefore both prioritise fixed civil recurrence over uninterrupted weekday naming succession.

This is an important distinction because it is easy to describe such calendars carelessly as “skipping a day”. They do not. Physical time does not skip anything. What changes is the sequence of civil labels assigned to successive sols.

The cost is calendrical and social, not physical.

The week is more than calendar machinery

That social cost deserves to be taken seriously because a week is not merely an administrative unit. It is a rhythm around which work, rest, education, family life, leisure, religious practice and transport can all become organised.

The seven-day cycle is deeply embedded in terrestrial civilisation in a way that most month-boundary arithmetic is not. Interrupting the civil weekday sequence therefore has a different character from making one month a sol shorter.

Imagine that the seventh weekday eventually became the principal weekly rest day in a Martian community. A shortened terminal civil week without that seventh label would immediately create a social question. Does the community move the rest day? Observe it according to a separate continuous seven-sol count? Compensate elsewhere?

A civil calendar cannot answer those questions on behalf of a future society. Employment law, religious observance and work-rest practice may all choose to relate to civil weekday labels differently.

That does not make the design issue disappear. It clarifies it.

Fixed recurring dates are attractive to administrators. Continuous weekly succession may be culturally or religiously important to other users. Neither concern is frivolous, and neither can be settled by arithmetic alone.

Šurán preserves the week

The obvious alternative is simply to let the weekday cycle continue. Every seventh sol receives the same weekday position regardless of month or year boundaries. No weekday label is omitted, and physical succession and civil weekday succession remain aligned.

The price is familiar from Earth. Month starts move through the week. Numerical dates change weekday. Reusable annual templates disappear. Recurring schedules have to specify both date and weekday rather than obtaining one automatically from the other.

That may be a perfectly sensible price to pay. Modern software makes floating calendars cheap, and humanity already knows how to live with them. There is a strong argument that a socially meaningful weekly rhythm should not be interrupted merely to make calendar templates tidier.

Josef Šurán showed that the choice is more interesting still. His 1997 work on perpetual Martian calendars considered adjustments made in days and in whole weeks. The important conceptual move was to ask not merely whether the calendar should be corrected, but at what scale.

A day-sized adjustment can keep the civil year close to the astronomical target, but a one-sol intervention is not a whole multiple of seven and therefore disturbs continuous weekly succession. A whole-week adjustment preserves the weekly sequence.

Šurán's preferred approach used years composed entirely of complete seven-sol weeks. A standard form contained 96 weeks:

96 × 7 = 672 sols

A designated skip-year form contained 95:

95 × 7 = 665 sols

The term skip week can sound more dramatic than the mechanism actually is. Seven physical sols do not vanish. Instead, the civil year contains either 96 or 95 complete weeks, and the year boundary is placed accordingly while physical time continues normally.

This produces an elegant result: continuous weekly succession and fixed date–weekday recurrence can coexist because every annual adjustment is itself a whole week.

That is a serious alternative to the Levitt–Darian approach. It simply spends the irregularity somewhere else.

The Martian year is about 668.6 sols. A 672-sol civil year runs several sols long; a 665-sol year runs several sols short. A suitable sequence can keep the long-run calendar aligned very accurately, but individual civil years move around the astronomical target by larger amounts than a design constrained to 668- and 669-sol years.

Šurán therefore preserves weekly continuity by allowing civil-year correction to occur in seven-sol blocks. Levitt and Darian preserve tighter individual year lengths by allowing selected civil weeks to contain only six weekday positions. A Gregorian-style design could preserve the continuous week and simply allow dates to drift. Other perpetual systems place special days outside the ordinary weekday cycle.

The fractional Martian year has not disappeared in any of them.

It has been put somewhere.

Where should the inconvenience live?

The week problem becomes clearer when the calendar names are removed.

There is no hidden winner in this table. It shows different allocations of inconvenience.

The continuous-week approach protects the integrity of the weekly sequence and accepts floating calendar dates. Levitt and Darian protect recurring date structure and allow the weekday naming sequence to be interrupted at selected boundaries. Šurán demonstrates that both continuous weeks and perpetual dates can be retained if the adjustment itself is made in whole weeks, at the cost of larger changes in individual civil-year length.

This is why the phrase perpetual calendar should be treated carefully. A perpetual calendar is not automatically more accurate, more humane or better suited to Mars. It simply preserves fixed relationships between dates and weekdays.

Whether that property is worth its cost remains a design judgement.

The operational attraction is nevertheless real. If Month 5, Day 17 always falls on the same weekday, a school timetable can repeat. A maintenance calendar can repeat. A reporting cycle can repeat. Printed and digital layouts need fewer variants, and users can infer weekday from date rather than looking it up.

Those benefits compound across institutions, but twenty-first-century computing has reduced their purely technical value. Calendar software is not distressed because 14 March changes weekday. Payroll systems can count Tuesdays perfectly well.

The remaining case is therefore partly human. There is a difference between a system that can calculate where a date falls and one in which a person already knows.

How much that difference would matter on Mars is not something we can establish today.

Regular in what way?

The week problem exposes how imprecise the word regular can be.

A continuously repeating seven-sol week is regular. A calendar in which every date always has the same weekday is regular. A civil year containing only whole weeks is regular. A civil year kept tightly around its astronomical target is regular in another sense.

Those properties cannot all be maximised simultaneously.

So whenever a calendar is described as “more regular”, the useful response is: regular in what way?

Levitt and Darian regularise the relationship between date and weekday. Šurán protects the weekly sequence itself while preserving perpetual dates through whole-week adjustment. A Gregorian-style system accepts moving dates in exchange for uninterrupted weeks and minimal intervention at calendar boundaries.

Each approach is coherent because each protects a different relationship.

The week problem therefore teaches something larger than whether Mars should have shortened weeks, floating dates or whole-week intercalation. It shows that calendar design is often less about eliminating irregularity than deciding where irregularity is least damaging.

A continuous week, fixed recurring dates and tightly bounded civil years are all reasonable objectives. Mars does not let us maximise all three at once.